Answer
The answer and procedures of the exercise are attached in the following archives.
Step-by-step explanation:
You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.
-2x + 3 > 3(2x - 1)
the inequality sign > means 'greater than'.
First simplify the right side of the equation by distributing the 3 over the parentheses:-
-2x + 3 > 6x - 3
Now add -6x to both sides of the inequality which gives us
-8x + 3 > -3
Adding -3 to both sides we have
-8x > -6
The next step is to divide both sides by -8 so x is isolated on the left side and this gives us the solution. However there is a rule with inequalities that if you divide the variable term by a negative the inequality is flipped. So in this case , greater that (>) becomes less than (<):-
-8x / -8 < -6/-8
x < 3/4 is your answer.
Answer:
Option A and Option B are not equivalent to the given expression.
Step-by-step explanation:
We are given the following expression:
Applying properties of exponents and base:
A. Using the exponential property 
, we can write:
which is not equal to the given expression.
B. Using the exponential property , we can write:
which is not equal to the given expression.
C. First we convert the radical form into exponent form. Then by using the property 
of exponent, we can write the following:
which is equal to the given expression.
D. First we convert the radical form into exponent form. Then by using the property of exponent, we can write the following:
which is equal to the given expression.
Option D and Option C are equivalent to the given expression.
Answer:
The radius of the scoop is r = 3.1 cm
Step-by-step explanation:
Since 3 gallons yields 90 scoops, and 1 gallon = 3785 cm³.
3 gallons = 3 × 3785 cm³ = 11355 cm³
So we have 11355 cm³ in 3 gallons which is also the volume of 90 scoops.
Since 90 scoops = 11355 cm³, then
1 scoop = 11355 cm³/90 = 126.2 cm³
Now, if each scoop is a sphere, the volume is given by V = 4πr³/3 where r is the radius of the scoop. Since we need to find the radius of the scoop, r, making r subject of the formula, we have
r = ∛(3V/4π)
Substituting V = 126.2 cm³, we have
r = ∛(3× 126.2 cm³/4π)
= ∛(378.6 cm³/12.57)
= ∛30.13 cm³
= 3.1 cm
So, the radius of the scoop is r = 3.1 cm
